Given:
The table of value of a linear function.
To find:
The linear function in slope intercept form.
Solution:
Slope intercept form:
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
Consider any two points from the given table.
It is clear that the linear function passes through the points (1,0) and (2,5). So, the equation of the linear function is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-0=\dfrac{5-0}{2-1}(x-1)[/tex]
[tex]y=\dfrac{5}{1}(x-1)[/tex]
[tex]y=5(x-1)[/tex]
Using distributive property, we get
[tex]y=5(x)+5(-1)[/tex]
[tex]y=5x-5[/tex]
Therefore, the slope intercept form of the given linear function is [tex]y=5x-5[/tex].
